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```					2D(3D?) cluster counting with
the digital TPC?

or

how to measure dE/dx without
measuring charges
Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 1
Ideal dE/dx measurement
Count number of clusters along track
cluster density should be proportional to dE/dx

Obvious problem:
cluster density is high (20 - 30 clusters/cm in Ar mixtures for
m.i.p.) = 1 cluster per 300 - 500 ìm
need device with high granularity to resolve them in space

Other problem:
Clusters sometimes have more than one electron:
1 el. 82.4 %
(TESLA-TPC, Ar/CH4/CO2, 93/5/2, calculation by HEED)
2 el.   6.9 %
3 el    2.0 %
how to avoid counting individual
10 el.   0.64 %
100 el.   0.0014 %
electrons of multi-electron clusters?

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 2
Classic dE/dx measurement
Widely used (because counting is difficult):
measure charge over some track length (sampling length)
"average" charge of many samples = dE/dx

Charge measurement requires:
electronics with good charge resolution, e.g. 8 bit or more
stable gain!!!
physics needs ÄG/G < 1/10ó(dE/dx)/dE/dx (better < 1/20)
< 0.5% (better < 0.2%) overall gain stability

some algorithm to remove unwanted multi-electron clusters
(delta electrons)
commonly used: truncated mean, remove a fixed fraction of highest charge
measurements, typically 20-30%, robust

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 3
dE/dx with GEMs
GEMs (Gas Electron Multiplier) + pads (typical size 5-10 mm)
are suggested as possible TPC-readout device
Nice detector for tracking, what about dE/dx?
Problem: GEMs show gas gain variations
local variations over the surface (static)
could make calibrations more complicated, not a problem in principle
time dependent (dynamic) variations due to charge-up effects
difficult to control and to calibrate, depend on background, might vary
within a bunch train

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 4
GEM gain variations
local gain variations:                     dynamic gain variations:

COMPASS GEMs

M. Hamann et al.(DESY/Univ. Hamburg)         C. Altunbas et al., CERN-EP 2002-008

➔   10% local gain variations          ➔   20-30% dynamic gain variations

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 5
Cluster Counting
Direct cluster counting avoids any problems with
gas gain instabilities
In theory  ultimate way to get dE/dx
30 clusters/cm * 120 cm track length = 3600 clusters = 1.7%
dE/dx resolution (TESLA-TDR: 4-4.5%)

Not a brand new idea:
previous attempts tried to resolve clusters in time:
slow gas / drift velocity (e.g. CO2) + good time and multi-hit resolution,
worked in lab + prototype detectors, never used in real big detectors for
physics

Now (that's new):
micro-pattern devices + small pads = high granularity could
make it possible to resolve them in space (2D), if time could be
Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 6
Could it work?
generate clusters/electrons (also long range delta electrons
using HEED (by I. Smirnov), take gas parameters (diffusion
etc.) from MAGBOLTZ (by S. Biagi)
track electrons through TPC volume, squeeze them through
GEM holes, apply gas gain (use Polya distribution for
fluctuations)
track all electrons created in gas amplification to a pad plane
(including diffusion, ódiffusion = 135 ìm over 2 mm)
(200 el. R.M.S. per pad, optimistic?)
apply threshold (1500 el.) and simply count number of pads
above threshold = clusters(?)
very CPU time consuming, need 50 Mill. electrons per full TPC
Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 7
Generated Electrons

HEED calculation
Track
(clusters)

some delta-
electron

TPC frame
(sideview)            GEM plane

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 8
Generated Electrons (close view)

65 keV
delta-electron

no diffusion                                          with diffusion
(ódiff,trans. = 1.1 mm, ódiff,long. = 4.4 mm for 250 cm drift and 4 T)

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 9

multi-electron
cluster

single electrons                pads (500 x 500 ìm2) above
at GEM plane                      threshold (1500 e-)

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 10
Questions
Counting with small pads seems to work
large pads: clusters can't be resolved
noise?
need low threshold to count a single electron after gas amplification on a
diffusion?
at large drift length (up to 250 cm at TESLA-TPC), multi-electron clusters
are spread by diffusion, individual electrons appear and are counted
again, not clusters

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 11

m.i.p., 0.6 GeV pions             high E tracks, 1000 GeV pions
(Fermi plateau)

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 12
Separation Power

simple pad counting,       classic dE/dx by charge
2.1 ó separation           measurement + truncated
mean, 2.1 ó separation
Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 13
Conclusions I
Separation power with cluster counting as good as
classic dE/dx by charge + truncated mean...
...but not better! (Factor 2 improvement expected)
Need to match:        average distance
between clusters
(375 ìm for m.i.p.)

(1.1 mm for 250 cm drift)               (noise  cost)

➔   Doesn't fit together for TESLA-TPC, too much diffusion!
➔   Electrons from multi-electron clusters dissolve and are
Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 14
Conclusions II
Cluster counting better than classic dE/dx by
charge needs:
gas with low ionisation
large distance between clusters
low probability for multi-electron clusters
low diffusion
either low diffusion gas or
short drift length

Helium(Neon?) mixtures could be a possible
candidate for successful cluster counting

Michael Hauschild (CERN), LCWS02, 27-Aug-2002, page 15

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